The Number of Prime Numbers and Twin Prime Numbers Is Infinite

A prime number graphic method is proposed. In the coordinate system, the prime number and its multiple points are represented by the prime number span-arc. Other points that cannot be determined as the prime number or the composite number are called undetermined points, so as to obtain the prime number generation process diagram represented by the hierarchical prime number span-arc. Then, prime factorial is defined to represent the product of generated prime numbers and used to segment all positive integers. Because the shape of the segmented prime number span-arc structure has periodic change rules, the generation process of prime number can also be transformed into the copy and sieve process of prime factorial segments. Because the copy and sieve process of prime factorial segments cannot filter out all the undetermined points, prime and twin prime numbers can be generated infinitely, which proves that the number of prime and twin prime numbers are infinite.